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Playing like you aren't interested is good in that they could realize how much they miss you
And if they don't then you weren't beating yourself up trying to win them back.

That is what I gathered. They say there are two sides to every story but I am usually good with reading between the lines and the human nature and how people react and so forth.
If you want her...

It sounds like she was overly insecure and made fights out of her insecurity.
Not sure cause you didn't really say what you would fight about.
But if someone in a relationship is insecure and...